Young's modulus, or elastic modulus (E), and Poisson's ratio (v) are two of the key mechanical properties of materials. Modem thin-film technologies have provided means for the development of coatings for various applications in mechanical, electrical, and biomedical engineering to protect the surfaces of components that bear load and transmit motion for performance and life enhancement. Such coating development demands an efficient and reliable, yet convenient, technology for the determination of the Young's modulus and Poisson's ratio of the coatings.
Currently, five techniques are commonly used for the measurements of the Young's modulus of thin-film coatings: (1) indentation, (2) beam bending, (3) vibration, (4) ultrasonic surface wave, and (5) scanning acoustic microscope (References: Bhushan 1999, Fischer-Cripps 2002, Schneider et al. 1992, and Fang 1999). Among these methods, indentation is the most popular technique, with which Young's modulus is often determined through the initial part of the unloading curve of an indentation data with sharp-pointed indenters (References: Loubet et al. 1984, Doemer and Nix 1986, Pharr et al. 1992, and Oliver and Pharr 1992). However, determining Young's modulus of a coating through this technique, at the macro, micro, or nano scale, has the following drawbacks. (1) The indentation data are indispensably contaminated by the response of the substrate materials under the coating to be measured. In order to minimize the substrate influence on properties measurement, the maximum indentation displacement (i.e. mutual approach or depth) is empirically limited to one-tenth of the coating thickness. This empirical requirement is not suitable for modulus measurement (References: Chudoba et al. 2002). Empirical and theoretical expressions have been proposed to account for the substrate influence on the measurement, e.g. References: Doemer and Nix 1986, Gao et al. 1992, and Men{hacek over (c)}ik et al. 1997. (2) The indenters have to be made sharp in order to have meaningful coating response under such shallow indenter penetration. The tip shape often deviates from the ideal one (rounded) and the indenters are easily damaged. (3) The indentation process is destructive. Dents are left in the sample after examination. In the neighborhood of dents, materials undergo the work-hardening process due to plasticity. For ceramic coatings, coating cracking usually accompanies the indentation process and affects the result of measurement. (4) For polymers, creeping may occur in the loading-unloading process and affect the result of measurement. (5) Existing models cannot accurately determine the contact area. For example, material pileup is significant in the indentation of thin-film and affected by the residual stress in the sample. The material pileup and plastic deformation under the indenter also change the coating thickness on the measurement site. (References: Lim et al. 1999). (6) Measured modulus is a modified Young's modulus, which equals Young's modulus divided by the difference between unity and square of Poisson's ratio.
Indentation displacement and force could be measured very accurately. For example, a commercial nanoindentation system could achieve the displacement resolution of 0.1 nm and the force resolution of 1 μN. The data analysis of recorded load-displacement indentation data is critical to the testing goal, such as determination of Young's modulus. Traditional indentation is in elastic-plastic range and Young's modulus is determined by elastic punch models (References: Loubet et al. 1984, Doemer and Nix 1986, Pharr et al. 1992, Gao et al. 1992, and Oliver and Pharr 1992) with the projected contact area and the slope of the load-displacement curve at the beginning of the unloading. Poisson's ratio for the sample is not determined but estimated. References (e.g., Wallace and Ilavsky 1998; Herbert et al. 2001) showed that Hertzian theory could be applied to determine the modified Young's modulus of a homogeneous sample by a spherical indenter in the elastic range. For thin-film coatings, References: Chudoba, Schwarzer and Richter (2000) showed the possibility to determine the modified Young's modulus by a spherical indenter working in the elastic range. An analytical solution for the indentation displacement due to an estimated (inaccurate) Hertzian pressure distribution is utilized to calculate the modified Young's modulus of a thin-film through a curve-fitting process of the load-displacement curve obtained from a depth-sensing measurement. However, the assumed Hertzian pressure distribution is not the true contact pressure between the spherical indenter and the coated sample, and because of the lack of the relationship between displacement and load a curve-fitting process has to be used. In all known indentation data analysis, Poisson's ratio is always assumed a priori.